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Tuesday, June 24, 2008

The Black Hole Information Loss Paradox

Prologue

I am constantly fighting information loss. Most importantly, there seems to get a lot of information lost in emails I write if those exceed one paragraph. What comes back then is stochastically distributed words that are uncorrelated with what I wrote. Anyway, as I had to realize yesterday, an inbox can also turn into a black hole if IT moves the folders but doesn't tell you how to reconfigure the ssh tunnel.

Not the Paradox

So, what is the black hole information loss paradox? The evolution laws in quantum mechanics are time-reversal invariant. (That does not include the measurement process, which does set limits to our knowledge). Initial states evolve into final states, the evolution is given by a Hamiltonian and is unitary. You can turn it back around. If you start with something it will go into something with probability one. The evolution is a one-to-one map. Unitarity is a fundamental property of quantum mechanics.

Now consider you have some matter distribution (e.g. a pressureless gas) and let it collapse (for simplicity assume it is spherically symmetric). That what you need to specify the precise state I will call information. The collapsing matter forms a horizon and becomes a black hole. The black hole no-hair theorem says that a black hole can carry only three parameters: mass, angular momentum, and electric charge. After the collapsing matter has settled down, this is the only information you can get from examining it. What happened to all the other information of your gas? All the details of that initial state?

Well, you could say, it's inside the black hole. So, no, collapse and formation of a horizon is not the information loss problem. You could say, the information still exists, but we are just disconnected from it. What's the problem with that? As long as my inbox still exists at least somewhere, that's okay, even if I can't access it.

The Paradox

But Hawking tells us black holes emit radiation, and this radiation is thermal. It is purely thermal, completely random, does not contain any information except its temperature. That is in contrast to e.g. the radiation of the sun. Which is for all practical purposes also thermal, but it does contain information 'in principle'. If you'd throw your bag of gas into the sun and you waited long enough you could 'in principle' extract its details again from the sun's radiation. Not so for the black hole. There is nothing to learn from the black hole's radiation.

Still you could say, well, if no information comes out, then it just stays inside.

But if Hawking is right, and the black hole radiates, then it loses mass. And eventually it is completely evaporated. There is nowhere left for the information to remain. The only thing that you have in the final state is that thermal radiation distributed over space. One could say then, well, black hole formation just is not time-reversal invariant. A singularity forms. A singularity is an attractor, whatever you started with it is always equally singular. There is no one-to-one map. Why is that a problem?

Well, the black hole formation could have happened for anything that forms or later falls into the black hole, and we know stuff behaves according to quantum mechanics. We have tested that experimentally uncountably many times. But if you consider an initial quantum state for the black hole, then no matter what precisely it was, the result is always thermal radiation, determined solely by the total mass, charge, and angular momentum. If you look at the final state, you can't trace it back to the initial state. It's not a one-to-one map. The evolution is not unitary, in conflict with the laws of quantum mechanics.

And that's the problem. The paradox. The apparent disagreement between general relativity and the laws of quantum mechanics. Hundreds, if not thousands of papers have been written about it since the solution to this paradox can be a key to our understanding of quantum gravity - whatever that theory looks like it should be able to resolve the problem.

Solution Attempts

A crucial aspect of this problem is that evaporating black holes are to excellent approximation classical objects for a very long time. Quantum gravity only can become important in the very late stages of the evaporation, then when the curvature comes in the Planckian regime, which happens only when the black hole's mass is about Planck mass (or its diameter of the order Planck length respectively.) Quantum gravitational effects thus can only influence the radiation in the last stages.

Various approaches have been tried to solve the problem, all have advantages and disadvantages (this is likely an incomplete list):

Solution: The evolution just is not unitary and information is indeed lost.

Problem: This is not only unappealing because it requires us to rethink how quantum mechanics works, it also leads to violations of energy conservation.

Solution: Black hole evaporation is modified in the late stages and black holes do not completely radiate but leave behind a stable remnant of approximately Planck mass that keeps the information.

Problem: Since the initial state that collapsed could have been anything, if the information is kept in the remnant that remnant must be able to carry an arbitrarily high amount of information. This leads you to conclude there must be an in principle infinitely large amount of black hole remnants with the same mass that are however different since they have different information content. This in turn results in the possibility to pair produce these objects infinitely in any arbitrarily complicated process where the energy is high enough. Even if the probability for the production of a single remnant is arbitrarily small, if there are infinitely many of them, you will still produce them. You could also emit them in black hole radiation itself: The high energy tail of the black hole spectrum might be exponentially suppressed, but if multiplied with infinity, black holes of arbitrary mass would decay instantaneously.

Solution: The information comes out with the radiation in the very late stages.

Problem: Then you have only very little energy left to carry all that information, which could have been arbitrarily much. This means per each unit of information you have a very small amount of energy to emit it which takes a long time, and you can't emit it simultaneously because if the wavefunctions overlap they'd be correlated. So that last stages would last very long (the more information needs to go out the longer) leading to quasi-stable black holes which cause essentially the same problems as the remnants of the previous point (their mass spectrum is not exactly degenerated but almost). Besides this, one would like to have an exact mechanism for how that happens.

Solution: Since the AdS/CFT conjecture relates black holes (in AdS space) to a quantum theory one knows is unitary on the boundary, this would mean the evolution in the bulk is also unitary.

Problem: As long as the conjecture is unproved one could equally well consider the information loss problem, if real, as a counter-example for the validity of the conjecture. (Also, I personally would find it unsatisfactory would this only work in AdS space).

Solution: Black holes have quantum hair that is not taken into account in the no-hair theorem.

Problem: Since the black hole can carry arbitrarily much information, one needs arbitrarily many quantum numbers to do that and a modification of our theories that can accommodate them. Why haven't we yet observed any of that? (Also, it's not clear to me how one would know that the black hole always carries enough of these new quantum numbers.)

From how I stated the problem above, it hopefully became clear why I think the problem is the singularity, not the horizon. The horizon is where information becomes inaccessible, but the singularity is where it gets lost. That's more or less by definition what a singularity is all about. The singularity is where the evolution becomes non-deterministic, where it can't be uniquely continued, it's where all initial states are crunched into the same divergence - already classically. Unlike the classical case however, here we have a scenario where the final state is without singularity again. Thus, the slicing has somehow to pass the singularity*.

But it is generally expected that some version of quantum gravity resolves the singularity and smoothens it out. Then, there is as far as I can see no reason why the evolution should be non-deterministic if the black hole eventually completely evaporates. If there is no slice on which initially different states run together, evolution from the initial to the final state has to be a one-to-one map. Determinism isn't sufficient, but necessary for unitarity. Either way, even if avoiding the singularity would imply unitarity, the problem then was not why, but how the information comes out.

The paper mentioned in the previos post by Dr. Who (Horowitz and Maldacena, hep-th/0310281) tackles this problem with the uniqueness of the state by imposing a final state boundary condition at the singularity which effectively transfers the information in the outgoing radiation. It's an interesting paper (thanks for pointing it out!), but the solution seems to me very ad hoc.

Bottomline

The black hole information loss paradox makes for an excellent topic over which to argue, because everybody has a different favourite solution. Of course I don't believe any of the above offered solutions, and of course nobody agrees with me. Anyway, here are the preliminary results of our poll "Do Black Holes destroy Information?":

From presently 146 people who voted, the majority, 37.7%, said "No, it comes out in the radiation.". A for me surprising 25.3% said yes, black holes destroy information. 16.5% including me voted "No, for other reasons.", documenting the mentioned plurality of opinions. Again surprising for me a full 8.9% voted for the remnant solution. (Surprising because whenever I say 'remnant' I get shouted down immediately.) Also 8.9% said 'Other' which includes the quantum hair option that I forgot for the poll, and 2.7% think the information survives in a baby universe.

If you didn't yet vote, vote now! If you did, has this post change your mind?

Epilogue

The one-hour phone call to Canada to figure out how to reconfigure my email client and tunnel through to my inbox goes on my mom's bill. I had to re-download 12,442 emails, but no information got lost.* Andrew: In the paper you mentioned by Zeh: gr-qc/0507051, he has an endstate with singularity, see Fig 1. In this case you can draw surfaces up to arbitrarily late - but finite! - times that do not reach the singularity, but this is not the relevant scenario in which the black hole is eventually completely evaporated.TAGS: BLACK HOLE, INFORMATION LOSS, PHYSICS

178 comments:

It is a big gotcha, and demonstrates the confusion between unitary and isomorphic operators. All unitary operators are isomorphisms, but not conversely. Further, for an operator to not lose any information it need only be isomorphic, not necessarily unitary.

So at least in infinite dimensional hilbert spaces one can find lossless linear transformations that are not reversible, truly weird.

Super article, Bee. Lots of good references as well (why do you bother with all this hard work??). I'll be returning to have a good read in detail.

Something that bugs me about all this is this key idea that the Hawking radiation is thermal. Everything depends on that - the whole paradox. So if that is so important then a vital first step is to consider why that radiation is/is not thermal.

So one way to imagine the Hawking radiation being generated is the pair of entangled particles appearing spontaneously from a quantum fluctuation of the vacuum, one being sucked into the black hole, the other being emitted as radiation.

Now, because these particles are entangled, you cannot treat the particles individually, they are inextricably linked. So we cannot get a complete description of the properties of one particle by examining it in isolation. However, because its pair particle has been sucked into the black hole we can now longer get any information from it. So we are forced into saying that the relevant particle property is random. This is all clearly stated in Lee Smolin's book "Three Steps to Quantum Gravity": "Each photon is correlated with one that is beyond her horizon. This means that part of the information she would need if she wanted to give a complete description of each photon she sees is inaccessible to her, because it resides in a photon that is in her hidden region".

But - here's the crunch - is it really random or does the entanglement still remain? This is where you can really help me, because I've got an idea and it has puzzled me for ages. I imagine an observer who falls into the black hole together with the particle that falls into the black hole. Now, for him, information about the pair particle outside the black hole is not lost because the event horizon only works in one direction - it does not prohibit information entering the black hole. If he performs an experiment on the particle entering the hole, and compares it with information he obtains about the particle outside the hole, he's going to find the particles are still entangled! Surely? So the information is not really missing for us (outside the hole), it's just inaccessible to us?

Although I am inclined to believe in the cft unitary approach by Hawking et al I've considered the following (not in the lit): The semiclassical black hole can not operate in the Planckian density regime, unlike a quantum black hole which can. When the semiclassical black hole has evaporated to 1.2 x 10^{19} grams it has a size very close to that of the classical hydrogen atom. If we consider that weak gravity (1/Mp^{2})~ 10^{-40} is a valid aspect of the Planck scale, then when the semiclassical black hole reaches the size of the classical hydrogen atom gravitational forces (or string tension maybe) should nearly balance out with the other gauge forces. However, if the mechanical potential of thermal fluctuations are greater (which may be possible) than the quantum gravitational forces then the semiclassical black hole dumps its energy in a huge correlated cascade. It might spit out 1 quantum black hole at this ultraviolent[sic] end.

Great post! I've always wondered why the discussion focuses so much on black holes. As I understand it, curved spacetimes aren't even necessary to produce the information loss problem.

A simple example of this is described by Wald (1994, ch. 7.3). Take a massless scalar field in plain old Minkowski spacetime. Define its initial (pure) state on a Cauchy hypersurface of Minkowski spacetime. Let the field evolve into a hyperboloid (as in this figure). Then the interior domain of dependence of the hyperboloid is correlated with radiation propagating out to infinity. So the final state of the field is mixed.

In sum: information is lost "at infinity," instead of "in a black hole," but it is lost nevertheless. So in what sense is this problem peculiar to curved spacetimes?

Maybe you can help me. I once tried learning a bit about black holes, and, if my textbooks were correct, that if you are outside of a black hole, you could watch the matter collapsing, but you wold never see the final collapse. Does this mean that when physicists say they see a black hole, they are actually reporting on matter which is in the process of collapsing into a black hole and inferring the black hole from that matter's point of view? (I gathered that someone falling in to a black hole would see all of the remaining history of the universe in finite time which is nicely symmetric).

So, how does Hawking radiation fit into this? If I am watching stuff falling into the hole and rapidly red shifting, do I also see an overlay of quantum noise and my image get both redder and noisier? Do I have to wait until the end of the universe to see the Hawking radiation?

If I throw a newspaper into a black hole, how long does it take, from my viewpoint outside the black hole, before it gets too red and noisy for me to read?

Am I really totally clueless here? Did I read some now discredited textbook? (I have an old book on Bohr's theory of the atom written just before quantum mechanics, and it has really neat orbital diagrams).

I'm also not convinced that Hawking radiation is thermal. From a distant observer's point of view, matter falling into a black hole never crosses the event horizon - it just gets increasingly redshifted. Now, if a Hawking pair is created at the horizon and one member escapes into free space within finite time, the distant observer must see it cross the path of infalling matter, which gives ample opportunity for the infall to imprint information on the Hawking radiation. If this holds for the distant observer, should it not also hold for all POVs?

A black hole's event horizon has an outward-facing blackbody temperature inversely proportional to BH mass. Is there any time in cosmic evolution when a created BH would be warmer than its surroundings? If not, no BH can evaporate faster than it feeds and further cools, and there is no information loss paradox.

A one solar mass BH emits at 60 nK - no evaporation. A one lunar mass BH emits at 2.7 K in equilibrium with the CMB - no evaporation. Primordial BH could be much smaller and hotter, but they were formed in much hotter surroundings - no evaporation.

When the LHC makes a baby BH there will be an information paradox as it evaporates. The universe then instantaneously uncreates. Uncle Al is the spoon.

I didn't get an answer to my question in the other BH thread, so can anyone explain why the following isn't (or is?) relevant to what is "lost" by falling into a BH: What I have read is: to an outside observer, the flow of rate for the falling body is red-shifted/slowed down more and more, asymptotically as it approaches the horizon. Hence, it never really falls through and nothing about it is really totally lost (?) at any moment *we* can define.

How a limit for us in all eternity can be consistent with the body's time moving past that is already perplexing, but in any case how does the above issue affect the loss of information in a BH? I mean, if we can always see the object in principle, however much red-shifted, why is there a loss to worry about?

Bee:Interesting comments by the lay people here and hopefully you will attempt to address them. I also think there maybe something suspect about the Hawking radiation calculation. The math maybe (is) correct but the physics maybe suspect. Until something like this is actually confirmed in the lab or by cosmic measurement then the physics should be viewed as just spectulation.

BH evaporation is critically tied to virtual particles. Are these particles real? They are if a BH evaporates. If these vitual particles are real then how do we account for the CC being 60-120 orders of magnitude too small using the same QFT that predicts BH evaporation? I see these two issues as being related.

Well, if "ad hoc" is the worst thing about it, it is way ahead of all other proposed solutions! I guess the point is: granted that all proposed solutions are unsatisfactory, which of them is most worth following up?

By the way, you forgot to mention Mathur's "fuzzballs".

http://arxiv.org/abs/0805.3716

I think that idea is *really* way out, but it seems to be getting some attention. [Like you, I am convinced that the problem is with the singularity and not with the event horizon, but who knows....]

I have never understood the argument that non-unitary evolution (which I agree is very unappealing) leads to loss of energy conservation. If you can explain it simply, and have time, I would really love to see it.

I would believe that generic non-unitary evolution leads to loss of energy conservation, but the laws of physics seem to be anything but generic.

I also voted No For Other Reasons, mainly because the unspoken constraint of only considering objectively existing long term classical black holes, rather than the observables out of which these are constructed, always bothers me.

I am not actually sure what it is that's bothering you. There is the issue that many people apparently like to work with eternal black holes. I never really understood what that's supposed to be good for since these don't exist anyway. But Hawking's calculation is for a collapsing system. Indeed one can see rather easily that if the system is not collapsing then, according to his calculation, there is no radiation. (That's not so surprising since the system is time-reversal invariant.) Best,

Yeah, I indeed like the paper you mentioned. It's very similar to where my thoughts were going with the problem that the singularity is a singularity is a singularity without further details. I would want to remove it and have a state that carries information, they instead put the information on the singularity, in spirit that's pretty much the same. The problem is though that I see no real reason as to why or how a singularity should come in infinitely many different versions. In fact, if I try to come up with a definition of singularity that does not include anything space-time related (because space-time possibly isn't even a meaningful concept in this region) then I'd say the very characteristic of the singularity is just that it is non-specific.

Regarding the fuzz-balls. Yeah. Now that you mention it, I forgot another branch of solution attempts, that's all those who temper with locality. I don't like the fuzz-balls, the problem is as far as I can see that one needs a modification of black holes at the horizon size, and that is for large black holes at arbitrarily small curvature, ie far away from where you'd expect any qg effects. If you let collapse something and it forms such a horizon at very low density, I can't see a good reason why it would suddenly fuzz.

That is for the case of the non-evaporating black hole that you can see the stuff until time goes to infinity. As I wrote in the post, if the black hole doesn't evaporate, you don't have a problem. In the evaporating case however, if you take time to infinity there is no black hole left. All you have is thermal radiation. The black hole is gone in finite time (though that might be a very long time). Best,

That is correct. It is very much a problem 'in principle'. I mean, even if all the information is in the Hawking radiation, you could hardly collect it all anyway. The PBHs would evaporate later when the soup has cooled. Best,

I did read only a few the solution approaches, but suppose you cannot transform to the initial state, because the Black Hole lacks a unitary rotation: could this not just be a result of the singularity of a Black Hole ?

In other words: is the Quantum Theory of a Black Hole somehow comparable to non-renormizable Quantum Theory, where the non-renormizability is created because we cannot find an intermediate state between the creation of a black hole and the final state being a Block Hole ? By the way what is the initial Quantum state of a black hole ?

SSH tunnels are awesome. I have a system configured to block all external & nonlocal VNC access, so I instead make a tunnel using putty and use VNC through that.

Back to physics..

Going back to step 0 in the original part of the post: The evolution is unitary and governed by the Hamiltonian.

Why is it that information is the same way? Is there a particular reason that information has to be knowable?

There is not an especially large amount of concern about the uncertainty principle - you can't know the state of a system to arbitrary accuracy.

Can you say why it would be unreasonable to assume there is no requirement for information to be knowable at all times?

I do not believe I am restating the first resolution, unless 'information' means the state of the system as well. I doubt that because the state of the system is not knowable in general, but as usual I can and probably will be wrong. In which case, whoops.

On a related topic, why is the the first attempt at resolving the paradox unsatisfactory? Given that the general subject of the topic is generalizing quantum mechanics to curved space time, can't we borrow a lesson from general relativity?

In general relativity, energy only exists under specific circumstances. The only one I know of is the requirement of a time-like killing vector / no time dependence in g_tt.

Is there a reason why tossing conservation of energy is especially bad? Or would that attempt at resolving things still not work in the specific cases of Schwarzschild/Kerr black holes where energy _does_ exist?

Other idle thought related to this:

In [b]classical[/b] GRA black hole with 'something' tossed in will eventually settle to a Schwazschild/Kerr/Reisser-Nordstrom type of black hole by. In other words, perturbations get sent away with gravitational radiation leaving the varying black hole 'ground states'.

Is the same thing necessarily true in the varying cracks at quantum gravity?

What I mean is that if I have a regular ol' Schwarzschild hole and toss an object in, will the settling process proceed the same way as in GR via emission of gravitational radiation and the requisite shenanigans with conservation of charge and angular momentum?

Or will Hawking radiation emission play a part? If it does, would the the radiation still be thermal and retain the paradox?

Had you read what I wrote you should have noticed the answer is that, yes, that's what I believe. The initial state can be everything that gets too much energy in a too small region of spacetime, may that be a collapsing gas or a highest-energetic two particle collision (you'll have to aim very precisely). Best,

What you say is entirely correct. If the collapsing (in-falling) matter emits radiation this will be more and more redshifted (since stuff will heat up when it gets accelerated towards the horizon it should generally emit radiation). In the case for a classical black hole, it would in principle look for the far observer as if it took infinitely long to form it. For the observer falling into the black hole, it would however only take a finite eigentime to cross the horizon.

The Hawking radiation has nothing to do with this radiation, it's an entirely different effect. The easiest way to picture it is as particle production in a strong background field. It is for the calculation usually assumed the only interaction between whatever quantum field you consider and the collapsing matter is through gravitational coupling. This is of course strictly speaking nonsense since the radiation should interact with/scatter on the matter, but it illuminates where the effect comes from.

As I also said to Neil above, in the case when the black hole evaporates you do not have an infinitely long time to see it form or to see stuff falling in. If you wait infinitely long, the black hole will be gone.

As to the question how long it would take until the newspaper gets unreadable, I have no clue, but it's pretty straigt forward to calculate how long it would take for it to be redshifted by some factor.

I have no idea how I can possibly make clearer what I have now repeated at least three times. There is nothing wrong with what you say. It just is not the problem. Please read my post: As long as the black hole is there, and there is some 'inside' where the other part of the entangled pair can be there is no problem. The problem only arises if the black hole is completely evaporated.

Yes, one can speculate that Hawking radiation is maybe not purely thermal and indeed does encode some information. The question then is how does that work? What is wrong with Hawking's calculation? Where does it fail, since it is an excellent approximation in the semi-classical regime? You can only modify it by quantum effects in the very late stages, with the problems I summarized in the post above. Best,

when the semiclassical black hole reaches the size of the classical hydrogen atom gravitational forces (or string tension maybe) should nearly balance out with the other gauge forces.

Sorry, I can't make any sense out of what you say. There is no way (without qg) one can stabilize the matter inside the black hole once it has collapsed, the standard gauge forces certainly can't do that. It would require an infinite pressure, that's what the Chandrasekhar limit and the singularity theorems are all about, there is no known way to prohibit collapse down to a singularity once you've passed that limit and certainly not after the horizon has already formed. Best,

“Hundreds, if not thousands of papers have been written about it since the solution to this paradox can be a key to our understanding of quantum gravity “

And here lies the solution for the paradox itself causes intelligent beings to write endless papers which have the effect to replace the information. This could serve to strengthen the arguments that QM is indeed non local:-)

More seriously, this is an excellent post, so good in fact that it will form for me and I expect many others to be the basis for more thought and study.

You might enjoy Joe's talk that I mentioned above (it seems to me you watch quite a few of our our recordings). He made the joke (not a quotation) that the paper production on the topic is very similar to the problem itself, there's a long time with random fuzz and then the information comes out in the end (well, in his opinion the problem is solved or as good as solved AdS/CFT wise). Best,

Yes, that's what I was saying in my post. It is usually assumed that the singularity is eventually gone with the black hole (there are very likely some people who'd disagree on that as well though). Best,

That is interesting, I hadn't heard of this example from Wald before, thanks for mentioning it. However, I don't quite understand what you are trying to say. So, this causes some outgoing mixed state. But the scalar field, hyperboloid or not, is still there. I don't see how this (entire) evolution can be non-unitary. I understand that it is not specific to curved spacetime you get this mixed state, but that, as I said in my post, is not the problem. As long as the information is somewhere, you don't have a problem. The problem only arises if the 'inside' vanishes without releasing the information. I just see no way you could do that in flat space (besides, if there is a field in that space-time, it is strictly speaking no longer flat). Best,

Yes I will indeed now have a look at Joe’s talk and while I wouldn’t say I watch a lot of the recordings I have watched several. To tell you the truth I don’t know how you people cope with it all. As for his remark it’s nice to hear that although I may not have the mind of theoretical physicists I might have some of the wit :-)

I said above in which way I used 'information', the conflict with QM is in the unitarity I don't see how one can lose information about the state but still have unitarity in the evolution of the wavefunction. I just guess that the 'unitarity paradox' didn't sound good. One can fiddle around with energy non-conservation, e.g. there's certainly limits to accuracy and if it stays below that that would be okay. However, I am not sure that would be possible, and even if I wouldn't particularly like that option. Think in terms of asymptotic states. You have some ingoing particles, spacetime is asymptotically flat. You have outgoing particles, spacetime is asymptotically flat. In between, you create a black hole that subsequently decays. I would want that process to conserve energy as all other scattering processes. Best,

Hi Bee, yes, I have read your post. I thought it was a very accurate survey of the situation -disappointingly hard to argue with! Bear with me, I understand what you're saying completely.

I don't think there's anything wrong with Stephen Hawking's calculation of radiation (as you suggest I'm suggesting), but that's not what we're considering here - we're just wondering where the information goes, and even Stephen Hawking seems a bit puzzled on that one. This is my take on things, slightly modified since last night.

As I suggested earlier, an observer inside the black hole would be able to get information from outside the hole, and would surely find the pair of Hawking particles (one on the inside of the hole, one on the outside) are still entangled. Let's say he performs a measurement inside the black hole and measures particle spin in the X direction for the particle he has inside the hole. Let's imagine there is another observer outside the black hole who is about to measure spin in the Y direction on the entangled twin particle outside the hole, and he's going to pass that information to our observer inside the hole (there's no restriction on information entering the hole).

Just to recap on quantum entanglement, the uncertainty principle states we cannot measure two noncommuting observables accurately - we can't know spin both the X and Y directions accurately, so as soon as the observer inside the hole performs his measurement in the X direction, there must be some instantaneous "poisoining" of the measurement outside of the hole (for a good explanation of noncommuting observables and this instantaneous "poisoning", see thisarticle by John Baez: "measuring one system should 'poison' any measurement of the other system, no matter what the distance between them").

So it would appear the particle inside the black hole has "poisoned" the particle outside the hole. But surely nothing can come out of a black hole? Well, to be more precise no **information** can come out of a black hole, and no information **has** come out of this particular black hole. Because of the random nature of quantum mechanics, you cannot use quantum entanglement to send information - hence, you can't use it for superluminal signalling. But even so, quantum entanglement can create apparently instantaneous connections across galaxies, and in this case it would appear it can create connections from the interior of a black hole to the outside (even though no information can escape using this method).

OK, you might say, what's the point of this if no information can escape from the hole, the paradox still applies? When the black hole evaporates, if the information has not been allowed to escape, where has it all gone (which is the crux of your argument, isn't it)?

Well, first of all it has become clear we are dealing with entangled particles being emitted from the black hole as radiation, and that's not really my definition of "random, thermal radiation". There's clearly more to those emitted particles than is usually suggested, and I think it's valuable and important to realise that.

OK, so how do I think the information escapes (and I'm a bit fuzzy on this bit, I'll admit, but here's the gist). If we go back to consider our experimenter inside the hole, as soon as he measures his particle in the X direction and finds it "spin up", then that instantaneously fixes the particle outside the hole to be "spin down" in the X direction. It's the process of "measurement" (however you want to define it) that fixes the values of the observables to clearly-defined values. When our observers inside and outside the hole have finished measuring all observables, then both particles have clearly defined values for all their observables. We have moved from a superposition state (a pure state) to a classical mixed state. The black hole event horizon is effectively completely irrelevant to this process! These could just as easily be two observers performing their experiments on two planets on different sides of the galaxy.

So here's the key, the information escapes because the information is never completely trapped! We absolutely have to remember we are dealing with entangled particles and we have to treat them as as single entity - even though they can be separated by a great distance or a black hole event horizon, and only ONE of the particles (i.e., one half of this single entity) is inside the horizon. When we have finished measuring both particles (and finding they have opposite values for X spin, opposite values for Y spin etc.) there is no more information to be obtained from the particle inside the hole, the particle outside the hole has all the available information about the particle inside the hole (albeit, all the observables values are opposite). The particle inside the hole can then be quite happily destroyed when the black hole evaporates as it contains no more information which has not been already extracted.

That is not a matter of agreement or disagreement what you say just does not make sense.

first of all it has become clear we are dealing with entangled particles being emitted from the black hole as radiation, and that's not really my definition of "random, thermal radiation". There's clearly more to those emitted particles than is usually suggested, and I think it's valuable and important to realise that.

Sure, I think everybody who works on the topic has realized that those particles are entangled. If you only have access to one half of them, you'll have to trace out the other half (inside) and the one you observe is indeed purely thermal. You find this in many places in the literature (I don't have time right know but can provide a reference later.)

When our observers inside and outside the hole have finished measuring all observables, then both particles have clearly defined values for all their observables. We have moved from a superposition state (a pure state) to a classical mixed state. The black hole event horizon is effectively completely irrelevant to this process! These could just as easily be two observers performing their experiments on two planets on different sides of the galaxy.

So here's the key, the information escapes because the information is never completely trapped! [...] When we have finished measuring both particles (and finding they have opposite values for X spin, opposite values for Y spin etc.) there is no more information to be obtained from the particle inside the hole, the particle outside the hole has all the available information about the particle inside the hole (albeit, all the observables values are opposite).

Yes, but you don't want information about the other pair of the entangled particles inside the black hole, you want to know the information of whatever collapsed to the black hole. That is the information you need to get into the radiation. Best,

Hi Bee, You said: "Sure, I think everybody who works on the topic has realized that those particles are entangled." Yes, I've just had a look at that slide presentation by Joe Polchinski you referenced and that states that the quantum state is entangled. I'm not an expert, so it was nice to see this clearly stated (glad I figured it myself!). I still feel that entanglement is crucial.

You said "Yes, but you don't want information about the other pair of the entangled particles inside the black hole, you want to know the information of whatever collapsed to the black hole. That is the information you need to get into the radiation." Yeah, I didn't say anything about that part, but I think I suggested a mechanism whereby entanglement could leak information out of a black hole (by straddling the horizon). You clearly don't agree! Like I say, I didn't consider the question of we can get information out of, say, a lump of lead that falls into the hole. I don't know if you saw this interesting suggestion in this New Scientist article. "The idea is that Hawking radiation is not random but contains subtle information on the matter that fell in", says Maldacena. Susskind: "Either we describe the stuff that fell into the horizon in terms of things behind the horizon, or we describe it in terms of the Hawking radiation that comes out." Very interesting thoughts. I do believe it comes out in the radiation.

I tend to view the AdS/CFT option (or something closely related) as the best and pretty much only viable explanation currently available.

1) Almost everyone believes that particular conjecture to be true, regardless of whether its not entirely rigorous *yet* (although a lot of people are getting very close to a full proof), since there are about 100 different proofs of concept and consistency checks. Also it works in hadron physics, so thats good enough for me.

Second, even if the paradigm is only true in ADS space, its sufficiently close a priori to flat or DS space to make one believe that holography should work in those domains as well, perhaps with a little twist. It would be completely bizarre that the entire physics changes in the limit of a physically miniscule, but negative CC and the regime where its exactly zero.

Third (assuming 1 is true), most of the other proposals fail miserably when put in an AdS background, since they do not encode the same physics as AdS/CFT (leading one to believe that they have made a mistake somewhere).

I voted for the destruction of information in black holes. We live with non-unitary evolution every day in the process of standard quantum measurement. There is not the slightest evidence for the multiworld interpretation of QM -- other than that it provides an ad hoc way of preserving the illusion of unitarity, albeit in a way that has no effect in our world. That argument is circular, so I am quite comfortable with non-unitary evolution.

The issue of information loss in black holes is made particularly stark if one considers a real case. A BH is made up of collapsed baryonic and dark matter, but baryon number is not one of the parameters we can use to describe the BH, so how is this simple piece of information preserved? Hawking radiation is essentially all photonic (except in the very last stages, the temperature is too low for anything else), What possible form of encoding could a naturally occurring physical process use to encode the baryon/dark matter ratio in the outgoing photons? None of the proposals for smearing information across the horizon, shunting it off into other universes, or whatever else, ever broach the real problem of giving some hint of the necessary new physics involved.

I see it also gives a description at the end of the article of how entanglement could leak information out of the hole, much in the way I suggested earlier: "Hawking radiation owes its existence to the weirdness of the quantum world, in which pairs of virtual particles pop up out of empty space, annihilate each other and disappear. Around a black hole, virtual particles and anti-particles can be separated by the event horizon. Unable to annihilate, they become real. The properties of each pair are linked, or entangled. What happens to one affects the other, even if one is inside the black hole."

"Seth Lloyd of the Massachusetts Institute of Technology believes that this phenomenon can be used to get information out of a black hole. His model, first suggested by Gary Horowitz of the University of California, Santa Barbara, and Juan Maldacena of the Institute for Advanced Study in Princeton, New Jersey, shows that when an in-falling Hawking particle interacts with matter inside the black hole, it sends information about the matter to its partner outside the black hole."

Hello Bee,Agreed! Sorry if I am not clear as I am not an effective communicator. I think the weird example presented just means that semiclassical states need quantum corrections in order to make the transition to quantum-gravitational states at high energies (or it collapses classically which would violate singularity theorem). In quantum gravity does not Heisenberg's principle ensure smearing of these states so that it is not clear there is a singularity or the states are non local in respect to the singularity?

Predictably LM has a dissertation already up on his website about this post. His active sonar picked up a tiny undercurrent or sentiment of unease about string theory's solution in Bee's post and zeroed in on it uniquely.

It is impressive how prodigous he is. Sometimes I get the feeling he must have written his book in about two days, given how fast he can get material to page.

As to Peter Shor's question, the answer that springs to mind is that the evolution operator is the "time-ordered" exponential time integral of the Hamiltonian. This operator is not formally unitary if energy isn't conserved. At least I think that is what is relevant here.

By the way, I notice that you make a lot of references to time-reversal invariance in your excellent post. I wonder if it necessary to invoke time-reversal invariance at all, since the real issue is whether unitarity is satisfied (though I am not sure about this). Often in statistical mechanics people confuse probablility conservation (unitarity) with time-reversal invariance.

Well Bee,I still say if death is like falling into a blackholemost of us are not gonna leave much of an imprint behind.

Sure some of us radiate whilst alive, and some of us may be remembered by close relatives or friends for a while, some of us may even be remembered thru a few generations if we say, write or do something awesome or memorable ...

but as the one in the blackhole, I'd be more concerned with what is on the other side - a Susskind multiverse (?)after all the universe I leave behind (outside the bh) is of little consequence to me, unless I'm returning into it thru a Smolin loop.

hm maybe the universe is cyclical, and we all (or at least some of us) return to the 'golden age'or maybe it is linear, and despite appearances to the contrary we are heading for the 'golden age' rather than some doomsday style armaggedon.

Yes, indeed, rather predictably. I said to Stefan yesterday, Lubos will produce one of his echos and proclaim I am stupid - and here we go. I am surprised though it took him a full 24 hours.

Anyway, needless to say, I know the horizon is a defining property of the black hole as I have said repeatedly on this blog at various occasions. I never said it's the singularity that defines the black hole, why would I, since I say I think the singularity is likely removed by qg effects.

Further, I never said that I doubt the AdS/CFT correspondence is true, I said it is unproved and even if Lubos seems to think so, 5,000 papers without a proof still don't make a proof. As to his claim that it is a logical fallacy to say one might as well believe information is just lost which would disprove AdS/CFT, please tell me what the logical mistake is. If you believe A it follows not B. On the other hand if you believe AdS/CFT it follows information is not lost. If you believe B it follows not A. Logically both is equivalent. If Lubos thinks there's more evidence on one side than on the other, that's a subjective impression. (I would even agree with him, but I don't think weighting evidence by number of papers is a good scientific procedure so you won't find arguments like this on my blog).

In this regard, I also encourage you to look the above mentioned recording of Joe Polchinski's talk. If I recall that correctly he indeed very openly mentioned exactly the same point. It is a very good talk and I can really recommend it. I wonder if Lubos would have addressed his 'criticism' to Polchinski?

Okay so I was just daydreaming, I mean literally daydreaming about black hole formation, wierd. And I thought of this:

Do particles every penetrate the event horizon? Or does fermi pressure cause them to accumulate with relativistic orbits on the event horizon?

So rather than imagining a neutron star collapsing inward, it acutally thins and spreads and shrinks like clay on a pottery wheel towards the event horizon; due to fermi pressure in the ground states.

So inside the event horizon there is no singularity, there isn't even curved space, just a flat (but very deep) metric. Where, like in QED, the depth of this flat metric can be measured as phase changes in the quantum states.

Peter and Peter, I think the precise statement relates evolution from pure to mixed states with violation of either causality or energy momentum conservation. Of course, there are assumptions...The canonical reference is the paper by Banks, Susskind and Peskin, "Difficulties for the Evolution of Pure States Into Mixed States".

Thanks for your answer. What I am somewhat dissatisfied with about it (and about all the other answers that I have seen) is that it assumes the laws of physics follow more or less the basic structure of quantum field theory, and we already know QFT is unitary.

If we need to radically change the fundamental basis of the laws of physics to understand quantum gravity, then I don't think any of these "proofs" hold water.

In order Peter Shor's question to be answered (if i have understood it correctly) you must prove that:

The expectation value of the energy (via hamiltonian operator) varies with time (i.e. energy not conserved) if the probability density (square of the absolute value of the wavefunction) varies with time (i.e. not unitary time evolution).

I don't think that this is the case but i haven't checked it to be honest.

How do we know that the radiation produced is actually "random" and does not contain the information? Is there a way to explain to a layman (me) how the black hole radiation is different from the example given with the sun and "bag of gas" thrown at it?

From my uneducated perspective both of these things seem too complex to be able to say emphatically that one is random and the other isn't.

Sorry in the previous comments I meant to say isometry (maintains sizes) instead of isomorphism.

Anyways in Functional Analysis a unitary operatory is defined as an invertible isometry. But the time shift operator on quantum states defined in a space time that has a finite beginning is an isometry, does conserve energy, but is not invertible on all the states, only on the sub-space of states that have zero desinties between the beginning of the space-time and the shift icrement.

I refer everyone to "Gravitation" by Misner, Thorne and Wheeler, specifically the Black Hole Dialog at the beginning of chapter 33. There we learn that an event horizon literally takes forever to form, but a gravitationally collapsing star will go dark quite suddenly as the horizon prepares to form. The last photon emerges within milliseconds of the star beginning to fade.

We then learn of the Surface of Last Influence. This thing is so insubstantial it makes a quantum vacuum seem like a neutron star by comparison. The Surface of Last Influence moves at the speed light towards the collapsing star and represents the last chance to influence the star before the horizon forms. If you fire your laser at the star before the surface passes through you, you might just bounce a few photons off of it. If you fire your laser after the Surface of Last Influence passes through you, your photons are time dilated so much that they never arrive at the star/hole. Of course since matter travels slower than photons it can't reach the star either after the surface passes through.

I conclude from this, that anyone whose arguments depend on a completed horizon or whose arguments depend on stuff falling into a hole interacting with stuff already there is just blowing hot air.

Everybody should go to the nearest physics library and read the Black Hole Dialog in "Gravitation". I mean that.

I think people who want to isolate the exact irreversable events associated with gravitational hole collapse should get some practice with less esoteric phenomena. When you can determine the exact irreversable events associated with say protein folding or quenching of hot steel, then you'll be ready for gravitational holes. I confess, that I myself, am not ready.

Is there a way to explain to a layman (me) how the black hole radiation is different from the example given with the sun and "bag of gas" thrown at it?

I guess I had a similar problem getting the point of the example with the "bag of gas" falling into the Sun when I read Sabine's draft.

If I understand it correctly now, the thing is that you could, in principle, follow the complete time evolution of the infalling gas and the radiation it does emit, using either classical or quantum laws for the description of the dynamics. Thus, it would be possible in principle to reconstruct the history of the "bag of gas".

On the other hand, Hawking radiation does emerge "without history" from the horizon. Maybe Sabine (or someone else) can correct me if I am wrong.

But for all pratical purposes, I do not see how one could distinguish both cases...

Strings existing in the five-dimensional space-time can even look point-like when they are close to the boundary. Polchinski and Strassler1 show that when an energetic four-dimensional particle (such as an electron) is scattered from these strings (describing protons), the main contribution comes from a string that is close to the boundary and it is therefore seen as a point-like object. So a string-like interpretation of a proton is not at odds with the observation that there are point-like objects inside it.

Dealing With a 5D World

A black hole is an object so massive that even light cannot escape from it. This requires the idea of a gravitational mass for a photon, which then allows the calculation of an escape energy for an object of that mass. When the escape energy is equal to the photon energy, the implication is that the object is a "black hole." See here.

Interactions between outgoing Hawking particles and ingoing matter are determined by gravitational forces and Standard Model interactions. In particular the gravitational interactions are responsible for the unitarity of the scattering against the horizon, as dictated by the holographic principle, but the Standard Model interactions also contribute, and understanding their effects is an important first step towards a complete understanding of the horizon’s dynamics. The relation between in- and outgoing states is described in terms of an operator algebra. In this paper, the first of a series, we describe the algebra induced on the horizon by U(1) vector fields and scalar fields, including the case of an Englert-Brout-Higgs mechanism, and a more careful consideration of the transverse vector field components.

Many people believe [this is a cop-out on my part, I believe it too but my confidence in what I am about to say is low!], anyway, I have heard several people say, that the *complete* evaporation of the hole is not necessary in order to have an information loss problem. Take one of those black holes that Bee doesn't like, the kind that you put in a box so it is in equilibrium with its Hawking radiation. Now throw in a system in a pure state into the hole. The hole will radiate thermally until it re-establishes equilibrium. I think it is fair to say that the thermal radiation is evidence that the pure state has apparently become mixed. So the complete evaporation of the hole is just an extreme case, a case where the information loss is most dramatic. But the problem is there long before that happens. One could probably clarify this by looking at Maldacena's famous paper

About the AdS/CFT solution of the problem: Suppose [a] that you believe in string theory [I do], then I think that it is reasonable to believe in AdS/CFT. Then it is reasonable to believe that there is no information loss for AdS black holes. BUT it is NOT reasonable to conclude from this that there is no information loss for realistic black holes. In particular, it is very silly indeed to argue that "black holes are local objects, so whatever works in AdS must work in the real world". Because AdS/CFT is *not* local in this sense --- if you believe that black holes are really "local" objects then you should not believe that AdS/CFT is relevant in the first place! As for the argument that "nothing special should happen" when you tune the AdS cosmological constant from small negative to small positive values, yeah, well, that's a great argument. I can use exactly the same "logic" to "prove" that ice can never melt. [Just tune the temperature up from -1 C to +1 C --- of course nothing special happens, right? Wrong!] The truth is that AdS is, on the scales where you use it to reason about the unitarity of bh evaporation, TOTALLY AND UTTERLY DIFFERENT to de Sitter space!

So does this mean that AdS arguments are irrelevant? Not at all! But you have to construct a convincing argument, not just wave your hands around and babble about how small negative numbers are not so different from small positive numbers!

Inside a very dense sphere of matter, for an observer far away, the distance between 2 any given particles inside a collapsing star would slowdown to infinity before reaching the critical density... So, I don't see the Surface of Last Inlfuence forming in a finity time, unless the particles tunnel to a place where a critical density can be achieved, that is, tunnel to the coordinates contained insided the horizon to be.

I agree with Gravitation if you use geometry to drive the collapse a star. But I have a problem to believe in that because, from the point of view of matter, nothing is mentioned.

For example, there is a step in the explanation, in which a given slice (ch. 32), the "mouth" of collapsing star is shut. I'd like to see an explanation of how or why (not) the matter content organize itself to allow such thing before that moment.

Even if I buy the geometric point of view, wouldn't it take an infinite time to an observer far way to see the "mouth" shutting? Because, if that is the case, the black hole would never form anyway, from the ponint of view of an outside observer.

Do me the favor and read this post, the references and the previous comments before you add redundant noise. This is no joke. They are there to be looked at, and I am not writing such a summary as a forum for random questions. At the very least, read my reply to Neil and Kaleberg above. I am not in the mood to repeat myself endlessly.Best,

Stefan, yeah, I think the reason we have to consider the Hawking radiation to be truly thermal is because it could be considered as resulting from quantum fluctuations, and the uncertainty principle means we have to consider it as fundamentally random (even though it would be entangled with particles inside the black hole, we would be fundamentally prohibited from obtaining that information, so we would have to consider the radiation as thermal).

A bag of gas falling into the sun would also be converted into thermal radiation, ie., maximum randomness "entropy", which can be described by a single temperature value (i.e., it carries no additional information). However, the bag of gas radiation would actually retain tiny correlations from our initial bag of gas. That would not be the case with Hawking radiation. So the bag of gas from the sun radiation would not, actually, have maximum entropy. That's my take on it, anyway.

Haelfix: even if the paradigm is only true in ADS space, its sufficiently close a priori to flat or DS space to make one believe that holography should work in those domains as well, perhaps with a little twist. It would be completely bizarre that the entire physics changes in the limit of a physically miniscule, but negative CC and the regime where its exactly zero.

Dr. Who: The truth is that AdS is, on the scales where you use it to reason about the unitarity of bh evaporation, TOTALLY AND UTTERLY DIFFERENT to de Sitter space!

The question of the Λ -> 0 limit is interesting, I was about to say the same as Dr. Who. It is not a priori plausible to me that the limit would change nothing. There are plenty of cases where conclusions hold for all ε > 0 but not for 0. Is there any evidence for that, I would be grateful for any reference/argument etc. I can't quite picture how it's supposed to work that an argument holds that rests on the presence of a (theory on the) boundary if there is no longer such a boundary. Best,

As I have said repeatedly above, it is of course correct that in a realistic scenario one does not have a Schwarzschild solution and no event horizon, instead you'd have to talk about dynamical horizons (see eg. this paper). I have no idea who specifically you are addressing your criticism to. Best,

Yeah, I guess that is an explanation which works quite well. For the case of the sun you have an evolution for the full system, it creates and emits radiation in standard processes and there is nothing unusual about it. For the black hole, you have the horizon that can be passed only one way. The thermal radiation is not created from the matter that collapsed (which is now inside and crunched to a singularity) and then goes off to the observer at infinity, but the radiation it is created at the horizon and does not carry information about the stuff that formed the black hole. Best,

By the way, I notice that you make a lot of references to time-reversal invariance in your excellent post. I wonder if it necessary to invoke time-reversal invariance at all, since the real issue is whether unitarity is satisfied (though I am not sure about this). Often in statistical mechanics people confuse probablility conservation (unitarity) with time-reversal invariance.

Glad you liked the post. When I say not time-reversal invariant I mean not time-reversal invariant. I am pointing this out because I can not make sense out of any explanations that rest on the Schwarzschild solution where there is no dynamical collapse. The production of the thermal radiation from the initial state is not time-reversible in the sense that after the black hole formed and completely evaporated you can't find out what it initially was, and this rests on there being a (classically) not time-reversible background. Best,

is an evaporating microstate blackhole really a blackhole because it has an 'event horizon'

is an evaporating (or even bursting) bubble in your fizzy drink an evaporating blackhole with an event horizon

If a massive or cosmic blackhole no longer has a massive singularity, is that not simply because the event horizon has stretched and the singularity is spread across the cosmos (aka universe) as mass & gravity, ie: galaxies, nebulae and everything within.

I'm sorry, I agree with your answer, but I was addressing Michael Welford, in which he said Gravitation arguments provided any kind of solution to this black hole paradox problem (ch.32 and ch.33) which I think do not. I'm sorry for the noise.

There is absolutely no experimental evidence for Hawking radiation. As Uncle al explained above correctly, the Hawking temperature for astrophysical black holes is extremely small, far too small to be observable, either directly or indirectly. The interest in the topic stems, as I was hoping becomes clear from my post, from the paradox that arises when one tries to combine quantum field theory with general relativity. It doesn't work as it should, and finding a solution could be a key to our understanding of quantum gravity, thus the large interest the paradox has received (and still recieves). Best,

In quantum gravity does not Heisenberg's principle ensure smearing of these states so that it is not clear there is a singularity or the states are non local in respect to the singularity?

I think we'd all like to know that, it is certainly what one would expect and there are hints pointing into this direction, but as far as I know the situation is not as clear as it needs to be to actually calculate what happens in this regime. Best,

ADS is a bulk spacetime. You can have small locally flat blackholes occupying somepart of that spacetime no problem, so long as everything averages out globally to lambda negative and say arbitrarily small. The keypoint is that the equivalent boundary theory is always unitarity, so it stands to reason those small and flat blackholes that live in the ADS space, must conserve their information *somehow*.

AdS/CFT doesn't tell you the exact dynamics of that process, that will require technology we don't yet have, but so long as you believe in the AdS/CFTs validity it strikes me as sort of really good handwavey proof of concept.

So I insist that it would be truly bizarre if a local object feels arbitrarily small global properties to such an extreme that a pillar of quantum mechanics fails. I can't accept that.

Answer - when it is thermal radiation observed 'cause of the Unruh effect.

i.e., if a inertial reference frame nice coherent pure state vacuum appears non-zero temperature thermal to an accelerated observer, then one has to wonder whether the thermal nature of Hawking radiation is misleading, there is actually information hidden in there.

ADS is a bulk spacetime. You can have small locally flat blackholes occupying somepart of that spacetime no problem, so long as everything averages out globally to lambda negative and say arbitrarily small. The keypoint is that the equivalent boundary theory is always unitarity, so it stands to reason those small and flat blackholes that live in the ADS space, must conserve their information *somehow*.

You said "Yes, but you don't want information about the other pair of the entangled particles inside the black hole, you want to know the information of whatever collapsed to the black hole. That is the information you need to get into the radiation." Yeah, I didn't say anything about that part, but I think I suggested a mechanism whereby entanglement could leak information out of a black hole (by straddling the horizon). You clearly don't agree! Like I say, I didn't consider the question of we can get information out of, say, a lump of lead that falls into the hole.

Well, but then exactly what problem are you considering? You clearly don't suggest any mechanism by which entanglement could 'leak out' information about the state that collapsed and formed the black hole, which would be necessary to solve the black hole information loss problem. Instead what you say is if you measure one pair of the entangled particles you know what the other one is. That is true, but you don't gain any insight from that which allows you to recover the lost information - unless you consider one of the above mentioned options to modify Hawking radiation that is.

I've just had a look at that slide presentation by Joe Polchinski you referenced and that states that the quantum state is entangled. I'm not an expert, so it was nice to see this clearly stated (glad I figured it myself!). I still feel that entanglement is crucial.

I was trying to make the point that Bee wasn't telling us all of the fundamentals and trying to rectify that. It may be that she considers professional physicists her main audience and it isn't worth all the work to help the rest of us catch up. I didn't intend for my post to be an argument for or against information loss, just as something that needs to be kept in mind. I guess I wasn't as clear as I should have been.

HI Bee,

My critique was kind of scattershot. Its targets do include your post. And by that I mean what appears on the computer monitor, not the post you intended to write, or your post augmented by your links. I won't risk antagonizing anyone else by naming them.

I downloaded the paper you linked to in your comment to me, and while I haven't fully absorbed all 101 pages of dense prose and equations, I can see how a horizon definition that: doesn't depend on what happens in the future, that isn't effected by the mathematical descriptions I choose, and that doesn't jump around discontinuously in response to continuous changes in the physical situation, might be more appropriate, for studies of Hawking radiation than some alternatives.

If you had just put the phrase "dynamical horizon" in your post I could have googled it.

I'm going to disobey my own admonition and describe a scenario. Perhaps you could comment on it's correctness, and say how our understanding is changed by dynamical horizons.

There is a black hole and an infalling sphere of gas and dust and me. The hole is truly enormous so as I fall in I won't be torn apart by tides and I have time to think about my fate. As I approach lightspeed, time dilation and the Doppler effect turn the trickle of low energy photons from the Hawking effect into a torrent of gamma rays.I wonder briefly whether a new horizon will form behind me before I'm dead of radiation poisoning. Information is being destroyed in my electronics, in my DNA and in my brain. This is degradation of a familiar kind so we can be sure that it is irreversible. My descent is eternal to outsiders, but the dissipation of the hole happens in a finite time so all of its energy will be radiated while I'm falling and I'm going to intercept my share of it. The final decay is glorious from my point of view, with an energy density not seen since the big bang. My only regret is that I didn't live to see it. Perhaps my ghost wonders whether my baryons will be destroyed in this glorious furnace. But how does my ghost hold on to his information?

From my vague understanding some people equate black hole entropy, with the von Neumann entropy measuring the entanglement between the inside and the outside of the event horizon. This seems to imply that as a black hole evaporates and shrinks, its event horizon area, and hence its (entanglement) entropy (between inside and outside) continuously decreases so that "information" is continuously flowing out of the evaporating black hole, and hence this seems to imply that the Hawking radiation must be of a form consistent with this. Does this make sense? I have no idea how such a thing would be made to work, but it seems it that this puts the problem on the whole evaporation process, not just the final burst. Any thoughts about this?

Hi Haelfix,First let me say that I regret the sarcastic tone of my first response to your post -- truth is, I was really responding to LM, not a good way to pursue reasoned debate. Anyway, this point you are raising is really at the crux of the matter in my opinion, because I agree with you that the AdS/CFT stuff really is the way forward. Where I differ is in how hard this way forward will be. Many string theorists [not just LM] believe or pretend to believe that AdSCFT has basically solved the problem already. As Bee notes, there is however a severe shortage of papers explaining exactly how this works. LM has provided his usual service: he is arrogant enough to stick his neck out, and the result is so vague and hand-wavy that it actually proves the point --- nobody knows how to export the results from AdS to the real world.

You say: "ADS is a bulk spacetime. You can have small locally flat blackholes occupying somepart of that spacetime no problem, so long as everything averages out globally to lambda negative and say arbitrarily small."

This is *not* how AdS/CFT works. And even if it were, your argument would only show that unitarity holds "on average". That would not satisfy most people!

You say:

"AdS/CFT doesn't tell you the exact dynamics of that process, that will require technology we don't yet have, but so long as you believe in the AdS/CFTs validity it strikes me as sort of really good handwavey proof of concept."

AdS/CFT gives something much better than handwaving: it gives you real reason to believe that black holes *IN ADS* [at least the eternal ones] preserve unitarity when some system in a pure state is thrown into them and then radiated out again. That in my opinion is a major step forward. *But* we need another step forward, we have to answer the question: what *exactly* is the relationship between *AdS* black holes and real ones? Until we know that, the AdS/CFT argument is incomplete.

You also say:

"So I insist that it would be truly bizarre if a local object feels arbitrarily small global properties......"

But that's exactly what AdS/CFT says! The CFT at infinity controls *everything* in the bulk: the two are physically identical. As it says in the Bible: "Not a single sparrow falls to the ground in AdS without your CFT's consent. As for you, every hair of your AdS head has been counted at spatial infinity; so do not be afraid of anything."

We investigate an important question of Hawking-like radiation as seen by an infalling observer during gravitational collapse. Using the functional Schrodinger formalism ... calculate the occupation number of particles registered by an infalling observer and demonstrate that the distribution is not quite thermal, though it becomes thermal once the black hole is formed in his frame.

The old version of string theory, pre-1995, had these first two features. It includes quantum mechanics and gravity, but the kinds of things we could calculate were pretty limited. All of a sudden in 1995, we learned how to calculate things when the interactions are strong. Suddenly we understood a lot about the theory. And so figuring out how to compute the entropy of black holes became a really obvious challenge. I, for one, felt it was incumbent upon the theory to give us a solution to the problem of computing the entropy, or it wasn't the right theory. Of course we were all gratified that it did. Black Holes and Beyond: Harvard's Andrew Strominger on String Theory

Strominger: That was the problem we had to solve. In order to count microstates, you need a microscopic theory. Boltzmann had one–the theory of molecules. We needed a microscopic theory for black holes that had to have three characteristics: One, it had to include quantum mechanics. Two, it obviously had to include gravity, because black holes are the quintessential gravitational objects. And three, it had to be a theory in which we would be able to do the hard computations of strong interactions. I say strong interactions because the forces inside a black hole are large, and whenever you have a system in which forces are large it becomes hard to do a calculation.

So how does all this come together into a physical theory? It turns out that the proper procedure is to construct every possible diagram allowed by the theory (for a given state of input and output particles and how they're moving) and add up the corresponding complex numbers. The result is essentially the "wave function" for that specific input-output state combination, and by squaring that number you can determine the probability that the given input will result in the given output. Doing that is how theorists at particle accelerators earn their keep.

I was about to say the same as Daniel, the infalling observer does not see an infinitely blueshifted spectrum as you seem to indicate.

My critique was kind of scattershot. Its targets do include your post. And by that I mean what appears on the computer monitor, not the post you intended to write, or your post augmented by your links. I won't risk antagonizing anyone else by naming them.

If you don't say clearly who or what you criticise it is merely annoying and not constructive. If your criticism was that I didn't explain in my post what a dynamical horizon is, please keep in mind this is neither a book nor a review paper, but a blog post. I have merely classified solution attempts and collected the basic references that I think are useful. You could have found the reference I gave you above in the mentioned paper by Ashtekar and Bojowald. Best,

I am not entirely sure what exactly your question is. For one I don't know in which way you refer to 'information' that is 'continuously flowing out of the evaporating black hole', but besides this I don't know why the outside would be entangled with the inside except for the infalling part of the Hawking radiation. It seems to me this requires some suddenly appearing non-local correlation when the black hole forms - such that there appears a correlation that previously wasn't there. Best,

B.

PS As I must have said more than a dozen times: did it occur to you that it is really confusing to have varios different 'Anonymous' in the same comment section? It can't possibly be so hard to come up with a pseudonym, at least add a number and make that Anonymous_23 or something else so I can tell you apart and you know who I am addressing my answers to. (Chose option Name/URL - you do not have to enter a URL)

Thanks for the nice words. I am not sure what you are saying with the Unruh observer. I too would suspect that the radiation isn't exactly thermal, but I don't see what this has to do with the Unruh effect. I think I mentioned it earlier that I find the often drawn analogy to the Unruh observer very misleading. The only concept that enters there is the acceleration whereas the important property of the collapsing black hole is its collapse. Best,

I don´t agree Michael's vision in its description. But I mut say that I agree with the aesthetical vision, since I think it's aproximately what someone would see as the horizon is aproached.

You are right when you say there is no blueshift, but because the energy should be conserved, an infalling observer should measure a more powerful hawking radiation to counter the slower time shift in relation to a far away observer, and each individual particle emited should have a higher frequency to counter the redishift measured far away.

Basicaly, as you aproached the horizon, you would see a stronger and stroger glare, until you perceive it as en explosive beam. The black hole would lose mass extremely fast in this process. If you survived this powerful beam, you would never touch the horizon anyway, because nothing would be left anyway when you get at the former center of the black hole.

I think it's aproximately what someone would see as the horizon is aproached.

That's not a matter of you think or I think but one can actually compute that. Unfortunately, I don't have the relevant book with me and can't look it up, so I can only hope that I recall correctly. I am reasonably sure the temperature does not diverge for the infalling observer if he crosses the horizon. One finds this calculation e.g. in Birrell & Davies, QFT in curved space. Best,

The point of the Unruh effect is twofold - one is that different observers can disagree on entropy; and the second is that a zero-entropy state to one observer can look thermal to another observer. Agreed a blackhole collapse is a completely different physical situation from an accelerated observer. But perhaps Hawking radiation needs to be examined for such a "paradox".

Perhaps observed radiation having a Planck spectrum is not enough to qualify it as thermal; Planck spectrum is talking only about the probability of occupation of photon states; I think we need to also show that photons are uncorrelated in any way. E.g., suppose I had a continuous bank of lasers, masers, etc., of various wavelengths, modulated in amplitude to produce a Planck spectrum; each of my lasers is phase modulated to carry MP3 music; is this thermal?

If there is a paradox for one observer (in this case the one at infinity) I would already call that a paradox. It would be more paradoxical (if not nonsensical) if it wasn't a paradox for every observer. I don't see how examining other observers could help with that. Yes, one needs to show the photon's are uncorrelated, but in Hawking's calculation there is just no way the radiation could carry information about the collapsing matter, it just doesn't enter the calculation. If one wants to get this information into the radiation (however you want to do that) one has to find a way how to. Best,

I don't agree about the statement 'only shows its on average unitary'. Theres a theorem afair to the effect that you can't do that. People tried to modify QM early on using ideas like that, and ended up hitting that nogo. I'd probably need to show this with a blackboard. But afaics, a CFT that is unitary cannot be decomposed into pieces that violate that condition.

As for the limit lambda --> 0, I agree its a hard problem, but the general expectation is that something replaces the correlators at infinity (say an SMatrix somehow). For DS space the relevant and robust observables are harder to identify in generality. I see this as a manmade technical problem, moreso than a physical one. Holography should go through in general given the only unambigous statement we currently have (ads/cft)

I did not agree with Michael, I did not say that there was a blueshift neither that temperature diverged. Just that it was visualy similar.

An observer far away sees the other infalling observer taking a finite time to cross the horizon, but because the black hole has a Hawking radiation, it will evaporate in an finite time. What I can see here it is that the infalling observer will see the black hole faster than what ever he does to try to cross the shrinking horizon. The temperature will be high, but not infinite.

To tell you the truth, in any of the scenery proposed, we are not even sure if any reasonable assumption was made. For example, the hawking radiation is restricted to the horizon and the obervers are classical, even though I am not sure in this case how a horizon, and thus a black hole could ever form. You see, people always use calculations that avoids too much non linearity, but GR is "extremely" non linear observers.

Once a dust cloud has condensed sufficiently that it is quark degenerate, wouldn't the (unkown) force(s) that caused inflation then dominate? Would that also place a lower bound on that amount of matter that is insufficient to push a dust cloud into a singularity, namely the whole universe?

I would imagine the formation would be like boiling water in zero gravity, a bubble (in this case a perfect vacum) forms in the middle of the quark degenerate matter and pushes outwards. Just inside this bubble is the event horizon.

As for approaching a black hole, presumably the momentum operators on a particle would have terms like the symmeterized contravariant derivative, whose commutators are the contracted curvature components. Thus the uncertainty in the momentum would increase with curvature. So as photon approaches an event horizon it spreads out in all direction along the sphere of the event horizon.

If you stick black hole area A(t) (varies in time) into a formula you get black hole entropy, E_1(t), say.

If you take a Hilbert space (of universe) and factor it into a product of two Hilbert spaces (inside and outside the event horizon) H_I(t), H_O(t), and a vector v(t) (wave function of universe), then you can stick H_I(t), H_O(t), v(t) into a formula to get entanglement entropy E_2(t), say.

So I thought some people equate E_1(t)=E_2(t). I wanted to know whether you think they should be equated. If not, wanted is it that is quantified by E_1(t)? And what do you think the value of E_2(t) is?

All this talk about observers is completely irrelevant to the problem. It's a scattering process with well defined asymptotically flat regions for times plus and minus infinity. If you want to talk about observers that's where you should place them. Inbetween there's an interaction happening, it's the same one does in quantum field theory all the time, but problem is with formation of a black hole the whole process doesn't seem to be unitary. Best,

Exactly! That's exactly why I think it isn't even surprising one "loses" information - because it wasn't put in to begin with. It is usually assumed the field interacts gravitationally only with the matter, so the only information it could possibly have is that of the gravitational field. But in the approximation used for the calculation not even this field enters with the necessary details, so why would anybody be surprised if it doesn't "come out" in the radiation? Best,

Okay, so no infinitely intense radiation. That said, I've been distracted all day wondering about dimensional scaling for Hawking radiation sails.

I One of the fundamental results in quantum computing comes from Rolf Landauer in the 60s and that is that information loss is a physical process and that it results in an increase in entropy.

This isn't just ivory tower stuff. Biochemists study the thermodynamic subtleties of DNA replication. Computer chip engineers are already beginning to design chips that operate reversibly. If Moores law for the scale of microprocessor circuits continues to apply, then we should be bumping into fundamental limits sometime in the 2020s.

Results in black hole physics that I have heard of, such as black hole entropy and Hawking radiation seem to be in wonderful accord with Landauer. So I don't understand why black hole information loss is considered paradoxical.

Of course, it is necessary to know how everything scatters, but I think the formation and accretion of matter to a black hole is fundamental to address this issue, because unlike other problems, information may be trapped inside the system forever or simply destroyed. So, you might never how to well define an assymtopticaly flat surface... So, I think studying the interactions may give you a clue of what to do.

Bee:You didn't respond to my previous post so let me try another angle. Does Hawking impose any particular restrictions on the black hole when he concludes that said BH will emit thermal radiation? How do partcles with mass get emitted thermally?

I was thinking of any residual electric charge that the BH carries. It can only be emitted through particles that carry electric charge; the lightest being an electron. So even if one electron is emitted in a sea of otherwise thermal photons is this still "thermal radiation"?

Sorry this is not Bee and yet this question is elementary enough for even me. In the Hawking view the BH doesn’t actually emit anything (except perhaps in a burst after many eons). Actually what is happening is that it is absorbing an antimatter particle from an anti/positive virtual pair with the positive one escaping to remain real. The anti particle has the effect to reduce the BH’s mass. This then is part of the dilemma, for even though the anti particle never actually escapes it is considered to carry information and thus the problem.

Phil:Sorry to disagree, but that is a model of what is happening. What is potentially observabled is thermal radiation emitted in 4pi steradians by the BH. So the question still remains: If a particle with mass is observed to be emitted by a BH in a sea of thermal photons is this apparent radiation thermal?

The thermal radiation depends on the spin statistic and also on the mass of the emitted particle species, both of which is relevant in the small energy limit, the spin also enters through the degrees of freedom. The spectrum is also technically seen not exactly thermal because a thermal spectrum would go all the way up to infinity, but the black hole can't emit particles with energies larger than it's own total energy. This is a limit that becomes important when the average energy of the emitted particles (ie the temperature) approaches the mass of the black hole (and therefore totally irrelevant for astrophysical black holes). Anyway, nothing of that helps you with the information loss paradox. Best,

I see that you already have responded to Cecil so I’m thus gratefully saved from any ham handed attempt. What I was going to say in brief is that he appeared to be mixing apples with bananas as to one not be applicable to the other, which appears to be your take.

Hi Bee, Phil:What I was attempting to suggest is the following. The paradox appears because BHs radiate according to Hawking's calculations which is apparently being accepted as correct given the physics model being used. But the calculation seems to be in disagreement with QM, a very well established and proven physical theory as opposed to BHs and BH radaition.

It just seems to me that the prudent thing to do would be to challenge the Hawking's physics model. My attempt at some examples was to suggest that if a BH radiates then all kinds of new physics would apparently be involved. The question about the proton decaying is just one example. The life time of a proton is > 10^33 years yet a BH with a lifetime of < 10-33 years that was comprised of protons would seem to be in violation of known physical limits.

I am asking a simple question: How many conservation laws (rules) that seem to have been validated by lab experiments will have to be violated IF a BH radiates?

“I am asking a simple question: How many conservation laws (rules) that seem to have been validated by lab experiments will have to be violated IF a BH radiates?”

You use two words here which have bearing on both the answer and the question; one being “seem” and the other “IF”. With this as the premise then of course everything is called into question. For instance I’ve said it could rest with QM being foundationally wanting, while others have said it relates to GR or SR or that with multi universes or an infinite universe all we need find is white holes (the other side of the looking glass). Still others say what’s the big deal with a little lost information for at earlier times what is missing now was only what is called potential so therefore there could be a equivalence to be found here resembling E=MC^2.

That is why it’s called a paradox for without a theory that can be supported by empirical evidence that’s all we will have. For me however that is both the point and the wonder of science, for we have a method which we both trust and hope will in time resolve it.

Shoot a light signal (information carrying light beam) into a black cavity (i.e., a blackbody) and watch the thermal radiation come out and try to decipher, even in this simple case, where the information went.

A similar way of doing what arun suggests is to take your red or green laser pointer and aim its beam at an incandescent light bulb (preferably frosted). Since the incandescent light bulb is a very good black body the dot of the intense beam disappears on the surface. This is really cool since the specific frequency gets redistributed in all the other spectral and thermal modes according to Planck's law. Try the beam on a quantum emission source such as a neon or fluorescent tube and the beam dot shows up because the source is not pure black body.

I think it is possible to derive the black hole entropy as a von Neumann entropy for entanglement between inside and outside, though I believe I recall there is some complication to it, some constant that has to be fixed. I don't know of anybody who believes the black hole entropy is zero. There are disagreements as to what the interpretation is of the black hole entropy, and - less commonly - also about what the entropy is, see the paper I mentioned above. Following Hawkings calculation one could eg try to argue that the resulting entropy is the entropy of the horizon, excluding the interior which is causally disconnected. Best,

I've just finished reading all your comments (126) and it's hard work. I think you should give people who don't read all the comments a break, even when they ask questions that you've already answered.

I don't follow all the arguments exactly but I'm impressed that your readers ask sensible questions and some make valid points. How do you avoid the real cranks that some other places attract?

OK, down to physics. You mention (somewhere in the middle of the commnets) that in dynamical situations one would need to look at a dynamical horizon rather than an event horizon.

Firstly, this is not strictly speaking true, since one can still have event horizons in dynamical situations, such as the Vaiday spacetime for example.

Secondly, and more importantly, I hope you realise that considering dynamical horizons rather than event horizons changes everything.

Event horizons are causal boundaries. They are always null hypersurfaces. Dynamical horizons (more properly marginally trapped tubes) are not causal and can be spacelike, null or timelike.

If they are growing they are spacelike, if the area is constant they are null and if they are shrinking they are timelike.

Timelike boundaries can be crossed in both directions. That means when the black hole is evaporating, and its "dynamical horizon" boundary is timelike, it can be crossed causally from the inside to the outside. Interesting huh?

It's kind of a chicken and egg problem since the black hole needs to evaporate for the horizon to be shrinking to begin with. But you are of course right, without the event horizon there are no globally causally disconnected areas.

I admittedly don't know how we managed to get such a nice and well-informed readership but you are right, it is really an interesting exchange we've had here. Best,

The other interesting thing about "dynamical horizons" is that one can derive a second law of black hole mechanics for them, just like one can for event horizons (Hawking area theorem). The first to show this was Collins way back in 1992 and Hayward did a similar thing with trapping horizons in 1994. (I should warn that all the names are different, apparent, trapping, dynamical etc, technically they all refer to different things, but they are all very closely related.)

Now this would seem to imply that one can associate entropy to either event horizons or dynamical horizons. In any given spacetime, for any given foliation, the areas of these two need not be the same (Vaidya example again). Areas are not the same implies entropies are not the same.

So if one wants to associate entropy to black hole areas, one had better choose between event horizons and trapping horizons (I'm going to switch now to calling them trapping horizons rather than dynamical horizons because Hayward's definition is broader than Ashtekar's (and he was prior)).

Do you really think this is a vital point for the information loss problem? I mean, I see that the understanding of the dynamical geometry is important for the thermodynamical analogy but I don't see how this really helps with the quantum fields in that background.

Well worth a read and I know it has helped a lot of people, especially in the GR community.

Hayward's model is a bit "ad hoc" and there are several things I would criticise about it. But his basic point is one can have spacetimes with black holes acting like black holes should, without singularities and without event horizons. If there are no event horizons (really one should say if the causal structure is trivial, as it is in Hayward's example) then there is no information problem. A similar point was made by Tipler and friends back in 2000.

I know the paper (I cited it in one of mine papers that however is still sitting in my drawer). I found it in spirit very simimlar to the Ashetkar + Bojowald argument, which is euqally ad hoc in that it just assumes such a solution exists. But even then, in both cases the problem remains to pinpoint a mechanism for information to come out. Simply saying what goes in must come out isn't satisfactory to me. Best,

There are close similarities between what Ashtekar and Bojowald are saying and what Hayward is saying. Ashtekar and Bojowald have a semi-explicit model that resolves the singularity (Loop Quantum Gravity), Hayward just puts it in by hand and does everything classically.

Now of course one can ask what happened to Penrose's singularity theorem (and various other theorems that appear in hawking and Ellis's book)?

Well, Penrose's theorem depends obviously a) there is a manifold everywhere such that one can talk meaningfully about geodesics, and b) the null energy condition.

Ashtekar and Bojowald violate a) since they have a "quantum spacetime" in the singular region (that they should admit they do not have full control over). Hayward does not violate a) he only violates the null energy condition.

Back in the early days, when Hawking and Ellis was being written and event horizons were being formalised as THE definition of black holes, everyone thought that the null energy condition was reasonable.

But it turns out, Hawking radiation violates the null energy condition. In fact, you need violation of the null energy condition for the area of any event horizon to shrink, since otherwise this violates Hawking's area theorem.

You also need violation of the null energy condition for the area of a trapping horizon to shrink. But fortunately hawking radiation does the trick. You can see this in Birrell and Davies eqn 8.60 for example and most explicitly in http://arxiv.org/abs/gr-qc/9604007.

Yes, I have had another mechanism to violate the energy conditions which was the content of my paper, the devil however is in the details. Ie you can postulate ad hoc all kinds of things but question is whether you can find a consistent theory to realize it in. The A+B approach seems to me insofar more reasonable as that there is a modification in the QG regime where you'd expect it. Best,

So you ask how this is relevant to information loss. Firstly, I think one should formulate a really rigorous defintion of information. Hayward calls it the "I" word. He's a real stickler for things that aren't rigorously defined (in case you've never met him).

There is an early defintion by Page (many years ago) in terms of entanglement entropy and horizon area. that's the best I've ever been able to find.

If you look very closely at Hawking's proofs of information loss you'll see the problem.

Firstly he confuses everybody by talking about uniqueness. Ashtekar and Bojowald call him out on that in the paper you refer to. It's not really relevant. You can have an infinite number of non-minimally coupled scalar fields and still have information loss by any other argument.

Then there's the argument about tracing over states inside the black hole that some of you posters refer to. This leads to pure states turning into fundamentally mixed states and hence violation of unitarity.

Mazur has a nice simple account of it in the introduction to one of his fuzzball papers. If there's no spacetime boundary for infalling particles to fall over (what would be the singularity in Schwarzschild) then there's no real reason to take a fundamental trace because the infalling particles can never really dissappear, they hve nowhere to go.

Then one could try to formulate the information loss in terms of some sort of past Cauchy problem.

Given a Cauchy surface to the future of the evaporated black hole, can I recover entriely the past? Well, obviously if there is a spacelike singularity (and an event horizon) then there will be a past Cauchy horizon unless I impose boundary conditions at/near the singularity.

Yes, we've been discussing that above, it's exactly the reason why I think if there's no singularity there's no problem. But despite my believe, I don't see how this explains why the evolution is unitary. Best,

You're right of course, no one has a fully concrete model to show it all works, but as i'm sure you're aware, people are working on it.

One thing is to show where Hawking wnet wrong. I think the Ashtekar/Hayward and friends have almost done that.

Another is to have a fully consistent model. Since the full picture needs a theory of what happens in the formally singular region, this almost certainly requires a theory of quantum gravity to be "fully consistent".

Anyway, I think it is important to see where hawking may have gone wrong and this helps debunk Susskind's Sherlock Holmes logic that locality must be violated "because it's the only available solution".

Well, I would say it would be hard for it not to be unitary if there is no singularity (all the "proofs" of non-unitarity break down).

If you want to know whether a state eveolved through the formally singular region can be evolved unitarily then that is, of course, a question that requires a TQG.

This is the question one might ask to AdS/CFT proponents.

I keep asking string theorists what happens when a ball of particles/strings is squashed to higher and higher densities. Some say that all the strings join up into one long string, but string theory isn't really set up to answer questions like that (and string theorists don't ask them).

They aren't. Many people just like to examine the case in which the black hole is just 'there' instead of forms and than evaporates. I expressed already above my opinion that this approach doesn't make sense. The problem in all cases however is that Hawking's calculation is and remains a damned good approximation and one needs to figure out where it goes really wrong.

You have the entropy of your collapsing star, and when the black hole forms you still have the entropy of your collpasing star, but now inside the horizon. When the Hawking radiation starts, it adds to the entropy. The entropy always goes up. there's no need to asign entropy to the horizon.

Think back to the original Wheeler-Bekenstein argument for asigning entropy to black holes. The event horizon was a causal boundary, what went behind was lost forever. The black hole area entropy was a measure of the unknowable interior state of the black hole (Bekenstein's abstract on his first paper).

If the black hole horizon is a dynamical horizon and not an event horizon, then the interior is not really gone forever and so no need to associate entropy.

I also think it's odd that people who think that information is conserved also feel that the horizon should have an entropy that measures lost information, because the information is never truly lost.

"The problem is you need something to happen already at arbitrarily small densities, not only at high ones."

Is this in reference to the formation of the event horizon? I don't think you need anything strange at small densities, just violation of the null energy condition should be enough. The light rays are not always converging. Hajicek talks about it way back when. http://prola.aps.org/abstract/PRD/v36/i4/p1065_1

Remember, the event horizon is tied up with the global causal structure. It is senstive to things like getting rid of the singularity, as in Ashtekar and Bojowald's model.

Very small changes can make a big difference to the global causal structure. Take Schwarzschild and add a single electron. Singularities changes from spacelike to timelike, new asymptotic regions open up, inner horiozns and Cauchy horizons form...

This little electron doesn't change the local physics much, but it changes the global structure in a big way.

Jst fyi, the fascination with static black holes that people have (and I agree with you it's not consistent) can be traced right back to Hawking and in particular to Birrel and Davies section 8.3, where they basically say that the radiation doesn't depend on the details of the collapse, so might as well consider the static case.

The big problem with denying that the area of a balck hole has an entropy, is all the calculations that explicity derive the Bekenstein-Hawking formula from microstate counting, Strominger and Vafa in string theory, Ashtekar, Baez and friends in (LQG) and all the other people that Steve Carlip lists in his papers on the subject.

I agree with you that people seem to have focused on misleading scenarios. I am not aware though that any specific definition of information is essential for the examination whether the evolution is unitary. Maybe calling it the 'information loss problem' is a misnomer to begin with. One could have called it the unitarity-violation-problem, but that doesn't sound like it would make a good headline. The problem with not having any modification already at small energy densities is that then you run into the mentioned problem of there being not enough energy left to eventually get the information out with. Best,

I see no real problem with letting calculations of the thermal spectrum stand.

For Hawking's calculation in terms of Bogolubov coefficients, he is tracing modes through the collapsing matter and out along the event horizon. To do this properly he should trace modes through a region that passes close to the point where the evaporating event horizon meets the singularity. Interesting things may happen there.

I don't think his tracing argument is robust unless there is some boundary.

Visser has already made the argument that Hawking radiation has nothing much to do with event horizons and doesn't even rely on the Einstein equations. http://arxiv.org/abs/hep-th/0106111

With the Hawking radiation, it is the spacetime that is evaporating, not the object that originally collapsed to form the black hole. So I see no reason why the state of the Hawking radiation shouldn't just rely on the state of of the spacetime near the horizon.

The interesting thing to look at is what happens to the ingoing negative energy states generated by the Hawking radiation when they catch up with the originally collapsed matter, near or at the centre of the black hole. No one ever really answers this question.

Of course when the black hole gets really small, and is evaporating really quickly into a region that is probably not well described by GR, then all bets are off.

The ingoing Hawking radiation has caught up with the centrally collapsed region, they've interacted in some fancy spacetime, then the horizon collapses down on top of them.

The interesting thing to look at is what happens to the ingoing negative energy states generated by the Hawking radiation when they catch up with the originally collapsed matter, near or at the centre of the black hole. No one ever really answers this question.

Yes, this is indeed the interesting question. Problem is one can't address it without knowing what state the collapsed matter will be in when it reaches Planckian densities. Horowitz and Maldacena

http://arxiv.org/abs/hep-th/0310281

basically postulate that problem away by imprinting some information on the outgoing state through a boundary condition at the singularity. But unless you do that you have the problem that when the ingoing part of the radiation reaches the inside matter (provided it is QG stabilized somehow) you need to find a way to get the information out of that (tiny) region with what little energy you have left then. Best,

"The problem with not having any modification already at small energy densities is that then you run into the mentioned problem of there being not enough energy left to eventually get the information out with."

So the information can somehow be measured in some number of bits? What is the minimal set of bits that I need to describe some gas of particles. Can I do this?

Things like total baryon number and the like? I don't see why baryon number can't be violated by black hole evaporation. It wouldn't necessarily make the evolution non-unitary.

Take Mathur's description of information loss (I like this paper but I don't much like fuzzballs for the reasons you give above).http://arxiv.org/abs/0803.2030

His argument is based on correlations, entanglement. there is no reference to conservation of bits, or to Cauchy evolution.

If Mathur's description of what the paradox is, is correct, then I see no reason why the entanglement can't come out right at the very end. Can you rigourously show that I need a large amount of energy for this entanglement?

If the process isn't one-to-one and 'squashes bits' into each other it can't be unitary, see above, the opposite could be the case though (i.e. even if you don't squash, it doesn't have to be unitary).

"No, you don't need a large amount of energy. But if you don't have the large amount of energy you need a long time with the above mentioned problems."

Why? I don't understand. Even if just one particle comes out right at the end, but it is entangled with all the other Hawking radiation particles that led to the evaporation, won't it still be unitary?

"If the process isn't one-to-one and 'squashes bits' into each other it can't be unitary, see above, the opposite could be the case though (i.e. even if you don't squash, it doesn't have to be unitary)."

I don't understand how you can conclude it won't be unitary if you squash enough, as you don't have a theory that is operable at these densities. I do agree that one needs to answer this question though. And therein is the crux.

How do you want to do that, you'd have to dramatically reduce the basis of the Hilbert space. Consider you create two entangled particle pairs, 1: up-down, 2: down-up, the first of which falls in, the other goes out. Now you need to encode 1: up 2: down, how do you do that with only one state? Besides this, that doesn't explain how the information from inside comes out, see above discussion with Andrew.

I have to go bed soon. It is late in my timezone. Let me know what parts of my arument you agree with and what parts you disagree with and I'll try to check back on Monday (going away for the weekend).

I think we agree that the distinction between event horizons and trapping horizons is important to the problem.

And we also agree that there are numerous places where Hawking may have "gone wrong".

And ultimately that the problem comes down to deciding what happens when you squash matter to very high densities.

Because, in your version of squashing you have squashed bits into each other and thrown some out. Think of bits as being positions and momenta in the classical version or whatever commuting quantum variables in the quantized version. You sqash them away, you don't any longer know what you had previously. Such a process can't be unitary.

OK, maybe one needs to think about this a bit more. But here's a quick example that might be interesting and help give an idea of what I am thinking of.

Forget black holes for a moment. Imagine I have a very large number of photons and a hydrogen atom. The photons all have energies that correspond to atomic transitions of the hydrogen electon. I would surely need a lot of bits to describe this state if I started out with a lot of photons.

Now let the photons fall into the hydrogen atom one by one in order, and the electron makes its transitions to higher and higher energy levels. I end up with a highly excited hydrogen atom and no photons.

Now suppose the electron makes a transition to its ground state in one jump. I end up with a hydrogen atom in its ground state and a single photon. I surely don't need many bits to descibe this final state. But it's all unitary (should be, it's flat-space QM).

Now maybe in many worlds or something I need to consider all the possible transisitions that the electron could make back to its ground state and I would end up with a many bit state again.

But in a single branch of the universe where the electron made a single jump, I don't need many bits to describe the final state.

(One might like to think of the implications of many worlds for black holes in general if one follows this line.)

I had a chance to look back over our discussion and read some of the references.

You agree with me that the issue is the non-unitarity, not any specific definition of information, but you still talk about the issue of "getting the information out". As long as the evolution is unitary, it doesn't matter whether the information gets out or not, as information is such a nebulously defined concept anyway. Do you agree?

What I'm saying is that without a non-trivial causal structure and somewhere to really lose stuff it is harder to argue that pure states evolve into mixed states than to just assume that a pure state always stays pure.

I had a look at your reference for the information taking a long time to get out of the Planckian sized black hole. Preskill's argument looks a bit woolly to me. I don't understand why the evaporation time is related to the size of a radiation sphere that collapses to a black hole and I don't understand why a Planck sized black hole would have to have the same entropy as a large black hole (it seems implicit in his argument).

Preskill's references make a bit more sense. Carlitz and Willey have a moving mirror analogy that may or may not work for the Planck sized black hole. Aharonov, Casher and Nussinov have a neat argument, but I'm still worried about defining things like wave-function overlap and emission rate for a Planckian region where I expect the notions of space and time to be modified and perhaps undefined.

I'm still surpised at the argument that says the temperature of the Planckian pseudo-remnant should be significantly less than expected and that the temperature should drop once the black hole gets small enough. Is this a theory indepedenet prediction of quantum gravity?

Ultimately it comes down to a question of how much one wants to trust arguments for how the Planck sized black hole should behave, based on analogies with known physical systems.

When considering information loss and the scenarios you listed, with arguments as to why they are unlikely, either one of the arguments breaks down somewhere or something happens that we haven't thought of yet. One should entertain the former possibility when things become "unclear" and things are uncalcuable.

One interesting reference that hasn't been mentioned yet in your comments ishttp://arxiv.org/abs/0801.1811basically claiming that information is not lost in the 2D CGHS black hole. Note that the agrument about causal structure plays a large part (their figure 2).

I like the (e-mail) tunneling solution. Most paradoxes (paradi?) are only so due to the frame of reference. Once the big(ger) picture is perceived, the paradox (not the information) disappears.

If the singularity is simply the end-point to another location (i.e., a "worm-hole" through space-time), then the information is not lost but re-located. It seems to be lost because we are not looking elsewhere for it to be emerging.

Do we know that the Hawking radiation is equivalent (thermally) to the mass and energy that have fallen into the black hole? If it is, then we have preservation of energy but loss of information. If it is less, then we may have preservation of information but loss of energy. If it is more, then we have broken all the rules but can have hope that someday at least our energy needs will be satisfied.

Energy conservation is an assumption. The calculation is done in a semi-classical approximation, meaning the background is fixed, meaning the energy extracted from it is not taken into account in the calculation but added later as a request of consistency, such that if radiation is emitted the mass of the black hole shrinks by the respective amount. This is also the reason why in this calculation the energy of the one particle pair technically seen is negative, since the background field is fixed, there is no other way to preserve energy. This however doesn't have a physical meaning, it just reflects the approximation used. Best,

a blackhole decays to a singular point in time, information is kept, until the instance before time began, and the universe has colapsed back to a singular itself,at which point, it has enough energy to overcome the reduced time colapsed information,and retreive it as latent radiation from within the time singular, which becomesinvisible, along with the information until the unversal singular is large enoughto break down the event horizon of that singular, until that time the event horizonhas not vanished, it has simply become to much random information prior to the universalsingular point to be distingushable.

"... te has to be a one-to-one map. Determinism isn't sufficient, but necessary for unitarity. Either way, even if avoiding the singularity would imply unitarity, the problem then was not why, but how the information comes out. ..."

The information comes out, when all singulars become one, that is at the point when there is enough energy to pass through all singulars ( even simulatiniously... ! ) and return with each singulars information.This is ....When the universe and time starts... nothing is lost, simply we dont have enough power to return the information due to radiation,gravity moving it beyond our ability to measure. -toad

BTW: the total lack of radiation through a horizon isn't always a feature of classical theory (although some of the logical and definitional structures that we've built up around general relativity certainly make it look that way).

In other contexts, the default behaviour of classical horizons tends to be indirect radiation. Imagine a plane of laser light projected at an acute angle into the surface of a rippling lake. The rippling of the lake's surface is entirely classical, but the illuminated line that intersects the surface fluctuates discontinuously, and jumps about. It never has a gap or break, and you can always divide photographs of the surface into regions "inside" and "outside" the line, ("a boundary has no boundary"), but you'll see "looplike" regions of line constantly breaking away and re-merging with the main section of line, discontinuously. The underlying physics is classical, but the resulting projection is quantum.

In the "acoustic metric" case, classical variations in local geometry due to local physics can cause the "effective" horizon for a given observer to snap discontinuously from in front of a particle to behind it. The effective horizon fluctuates and radiates in response to events that happen behind it. The local causal structure is preserved, but odd things appear to happen globally that can create the appearance of non-causality in a simple projection. If a model doesn't take these fluctuations into account, and assumes by definition that the horizon is static, then, if we use that horizon as our reference, the particle appears to snap discontinuously into existence somewhere outside the horizon-bounded region.

Although this is a classical effect, imposing a simplified (and not entirely correct) coordinate system onto it forces the radiation leaking through the fluctuating horizon to be described as the apparent end-result of non-classical particle-pair production processes ocurring outside the horizon, and you can model these statistically as Hawking radiation.

If there was a serious mistake or oversimplification in the structure of general relativity that resulted in it getting its horizon behaviour wrong, we'd expect to see exactly this sort of conflict arising between GR and QM, as a consequence of the mistake.

Hawking's already explored the possibility that the BHIP might be due to a fundamental structural mistake in current quantum theory (the "microcausality" thing - not a great argument, but someone had to look into it), IMO we should also consider the possibility of a fundamental structural mistake in general relativity.

Gilesgoatboy: I'm not sure where you got your impression from on what is the "leading" solution? In my previous post I was listing mechanisms for information recovery. It's not sufficient for that to claim information isn't lost, but you need to know when and how it comes out. For what I know it's still not entirely clear how information recovery is supposed to happen. Moshe wrote a nice post on this last year, you might find it helpful. Best,

I'd like to offer a way of thinking of Andrew's idea (using entanglement getting information out):

Let's say there is an electron inside th BH, which is called particle A.Then there is virtual particle pair B,C (of electron-positron or positron-electron).B falls into BH, and C gets out.

Now any measurement done over all three particles reveals information of A only.

E.g. the “measure the number of particles” measurement of [A,B,C], gives number 1 as a result.

Then, if the “measure the number of particles” is done separately inside (for [A,B]) and outside (for C) of BH, the sum of the results still needs to be 1. And as the particle C is real (single particle can not be virtual), the “number of particles” of [C] is 1. So “number of particles” of [A,B] needs to be 0. (when some-one “sees” particle C, he actually measures the “number of particles”, and the wave function of [A,B,C] collapses so that “number of particles” of [A,B] fixes to 0.)

All of the information of A is still in the system [A,B,C].

If we allow ourselves the luxury of thinking [A,B] now as a virtual pair (as the “number of particles” of [A,B] is 0, I don't see any other solution to them apart from virtual pair), measuring anything from [A,B] gives zero information, thus measuring C should contain all the information originally in A.

This has similarities with teleportation, but lacks the need of classical information. Or actually the amount of classical information needed is zero bits (as the [A,B] has no information, and in case of classical teleportation the measurement result of [A,B] (collapsed to a pure state) needs to be transmitted as classical bits).

The flavor of original BC pair could also be considered as quantum information:(|B=electron,C=positron> vs |B=positron,C=electron>). Or even wider, the type of elementary particle pair (electron, proton, photon, …) could also be unknown (but entangled between B and C (C = anti B)), and only be resolved only when B “annihilates” (if you like to call virtual particle disappearance as annihilation), which would fix the type of C.

[not entirely sure I should open my mouth, my resembling some kind of food more than a physicist] This might be the silliest proposition in the thread, and maybe it has been answered, but is it possible that the information gets separated from the mass at an early stage and remains outside the horizon? I'm not sure what problems arise from mass without the information to run it in reverse. I'm sorry if this is just noise.

That's an interesting question. You do not need mass to encode information, but you do at least need energy. However, you can use massless particles. That the collapsing mass gets rid of all information before it forms a horizon is commonly referred to as "bleaching." The problem with this is however, there is no reason why it should happen, and no mechanism that could possibly explain it since, as I explained above, for large black holes this is all physics that we know very well. Best,

Personally, I think that it is similar to a computer hard drive, where the information is just over-written. I base this idea off of the principle of "if a hydrogen atom is bonded to an oxygen atom, how do you tell what it was bonded to before that?". Simply put, the information changes once the energy/matter is released from the black hole.

Great reading, Bee. Thanks for helping to make the topic understandable.

If an electron falls into a BH, then the No Hair Theorem tells us that lepton number is not preserved by the BH. But if I am an observer outside the event horizon, then I never see the electron cross the EH. In fact any measurement I perform will tell me that the lepton number is preserved outside of the EH. (same thing is true for any "information").

As you point out in your Paradox/Not a Paradox section, the only problem occurs when the BH evaporates and the EH disappears. The information loss is a result of the evaporation, not the formation of a BH.

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